Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator

The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. The bound-state energies are given as zeros of a calculable function, if the potential is confined in a spherical box. For an unconfined potential the interval bounding the energy eigenvalues can be determined in a similar way with an arbitrarily chosen precision. The very accurate results for various spherically symmetric anharmonic potentials are presented.Comment: 16 pages, 5 figures, published in J. Phys

Who Underreports Smoking on Birth Records: A Monte Carlo Predictive Model with Validation

Research has shown that self-reports of smoking during pregnancy may underestimate true prevalence. However, little is known about which populations have higher rates of underreporting. Availability of more accurate measures of smoking during pregnancy could greatly enhance the usefulness of existing studies on the effects of maternal smoking offspring, especially in those populations where underreporting may lead to underestimation of the impact of smoking during pregnancy.In this paper, we develop a statistical Monte Carlo model to estimate patterns of underreporting of smoking during pregnancy, and apply it to analyze the smoking self-report data from birth certificates in the state of Massachusetts. Our results illustrate non-uniform patterns of underreporting of smoking during pregnancy among different populations. Estimates of likely underreporting of smoking during pregnancy were highest among mothers who were college-educated, married, aged 30 years or older, employed full-time, and planning to breastfeed. The model's findings are validated and compared to an existing underreporting adjustment approach in the Maternal and Infant Smoking Study of East Boston (MISSEB).The validation results show that when biological assays are not available, the Monte Carlo method proposed can provide a more accurate estimate of the smoking status during pregnancy than self-reports alone. Such methods hold promise for providing a better assessment of the impact of smoking during pregnancy

One-dimensional non-interacting fermions in harmonic confinement: equilibrium and dynamical properties

We consider a system of one-dimensional non-interacting fermions in external harmonic confinement. Using an efficient Green's function method we evaluate the exact profiles and the pair correlation function, showing a direct signature of the Fermi statistics and of the single quantum-level occupancy. We also study the dynamical properties of the gas, obtaining the spectrum both in the collisionless and in the collisional regime. Our results apply as well to describe a one-dimensional Bose gas with point-like hard-core interactions.Comment: 11 pages, 5 figure

Ferroelectricity and ferromagnetism in EuTiO3 nanowires

We predicted the ferroelectric-ferromagnetic multiferroic properties of EuTiO3 nanowires and generated the phase diagrams in coordinates of temperature and wire radii. The calculations were performed within the Landau-Ginzburg-Devonshire theory with phenomenological parameters extracted from tabulated experimental data and first principles calculations. Since bulk EuTiO3 is antiferromagnetic at temperatures lower than 5.5 K and paraelectric at all temperatures, our goal was to investigate the possibility of inducing the ferroelectric and ferromagnetic properties of EuTiO3 by reducing the bulk to nanosystems. Our results indicate that ferroelectric spontaneous polarization of ~0.1-0.5C/m2 is induced in EuTiO3 nanowires due to the intrinsic surface stress, which is inversely proportional to the nanowire radius. The spontaneous polarization exists at temperatures lower than 300 K, for the wire radius less than 1 nm and typical surface stress coefficients ~ 15 N/m. Due to the strong biquadratic magnetoelectric coupling, the spontaneous polarization in turn induces the ferromagnetic phase at temperatures lower than 30 K for 2 nm nanowire, and at temperatures lower than 10 K for 4 nm nanowire in EuTiO3. Thus we predicted that the EuTiO3 nanowires can be the new ferroelectric-ferromagnetic multiferroic.Comment: 22 pages, 5 figures, 1 tabl

Domain wall conduction in multiaxial ferroelectrics

The conductance of domain wall structures consisting of either stripes or cylindrical domains in multi-axial ferroelectric-semiconductors is analyzed. The effects of the domain size, wall tilt and curvature, on charge accumulation, are analyzed using the Landau-Ginsburg Devonshire (LGD) theory for polarization combined with Poisson equation for charge distributions. Both the classical ferroelectric parameters including expansion coefficients in 2-4-6 Landau potential and gradient terms, as well as flexoelectric coupling, inhomogeneous elastic strains and electrostriction are included in the present analysis. Spatial distributions of the ionized donors, free electrons and holes were found self-consistently using the effective mass approximation for the respective densities of states. The proximity and size effect of the electron and donor accumulation/depletion by thin stripe domains and cylindrical nanodomains are revealed. In contrast to thick domain stripes and thicker cylindrical domains, in which the carrier accumulation (and so the static conductivity) sharply increases at the domain walls only, small nanodomains of radius less then 5-10 correlation length appeared conducting across entire cross-section. Implications of such conductive nanosized channels may be promising for nanoelectronics.Comment: 39 pages, 11 figures, 3 tables, 4 appendice

Roto-flexoelectric coupling impact on the phase diagrams and pyroelectricity of thin SrTiO3 films

The influence of the flexoelectric and rotostriction coupling on the phase diagrams of ferroelastic-quantum paraelectric SrTiO3 films was studied using Landau-Ginzburg-Devonshire (LGD) theory. The phase diagrams in coordinates temperature - film thickness were calculated for different epitaxial misfit strains. Tensile misfit strains stimulate appearance of the spontaneous out-of-plane structural order parameter (displacement vector of an appropriate oxygen atom from its cubic position) in the structural phase. Compressive misfit strains stimulate appearance of the spontaneous in-plane structural order parameter. Gradients of the structural order parameter components, which inevitably exist in the vicinity of film surfaces due to the termination and symmetry breaking, induce improper polarization and pyroelectric response via the flexoelectric and rotostriction coupling mechanism. Flexoelectric and rotostriction coupling results in the roto-flexoelectric field that is antisymmetric inside the film, small in the central part of the film, where the gradients of the structural parameter are small, and maximal near the surfaces, where the gradients of the structural parameter are highest. The field induces improper polarization and pyroelectric response. Penetration depths of the improper phases (both polar and structural) can reach several nm from the film surfaces. An improper pyroelectric response of thin films is high enough to be registered with planar-type electrode configurations by conventional pyroelectric methods.Comment: 35 pages, 9 figures, 1 appendix, 1 tabl

Conductivity of twin walls - surface junctions in ferroelastics: interplay of deformation potential, octahedral rotations, improper ferroelectricity and flexoelectric coupling

Electronic and structural phenomena at the twin domain wall-surface junctions in the ferroelastic materials are analyzed. Carriers accumulation caused by the strain-induced band structure changes originated via the deformation potential mechanism, structural order parameter gradient, rotostriction and flexoelectric coupling is explored. Approximate analytical results show that inhomogeneous elastic strains, which exist in the vicinity of the twin walls - surface junctions due to the rotostriction coupling, decrease the local band gap via the deformation potential and flexoelectric coupling mechanisms. This is the direct mechanism of the twin walls static conductivity in ferroelastics and, by extension, in multiferroics and ferroelectrics. On the other hand, flexoelectric and rotostriction coupling leads to the appearance of the improper polarization and electric fields proportional to the structural order parameter gradient in the vicinity of the twin walls - surface junctions. The "flexo-roto" fields leading to the carrier accumulation are considered as indirect mechanism of the twin walls conductivity. Comparison of the direct and indirect mechanisms illustrates complex range of phenomena directly responsible for domain walls static conductivity in materials with multiple order parameters.Comment: 35 pages, 11 figures, 3 table, 3 appendices Improved set of rotostriction coefficients are used in calculation

Thermodynamics of nanodomain formation and breakdown in Scanning Probe Microscopy: Landau-Ginzburg-Devonshire approach

Thermodynamics of tip-induced nanodomain formation in scanning probe microscopy of ferroelectric films and crystals is studied using the Landau-Ginzburg-Devonshire phenomenological approach. The local redistribution of polarization induced by the biased probe apex is analyzed including the effects of polarization gradients, field dependence of dielectric properties, intrinsic domain wall width, and film thickness. The polarization distribution inside subcritical nucleus of the domain preceding the nucleation event is very smooth and localized below the probe, and the electrostatic field distribution is dominated by the tip. In contrast, polarization distribution inside the stable domain is rectangular-like, and the associated electrostatic fields clearly illustrate the presence of tip-induced and depolarization field components. The calculated coercive biases of domain formation are in a good agreement with available experimental results for typical ferroelectric materials. The microscopic origin of the observed domain tip elongation in the region where the probe electric field is much smaller than the intrinsic coercive field is the positive depolarization field in front of the moving counter domain wall. For infinitely thin domain walls local domain breakdown through the sample depth appears. The results obtained here are complementary to the Landauer-Molotskii energetic approach.Comment: 35 pages, 8 figures, suplementary attached, to be submitted to Phys. Rev.

High stakes and low bars: How international recognition shapes the conduct of civil wars

When rebel groups engage incumbent governments in war for control of the state, questions of international recognition arise. International recognition determines which combatants can draw on state assets, receive overt military aid, and borrow as sovereigns—all of which can have profound consequences for the military balance during civil war. How do third-party states and international organizations determine whom to treat as a state's official government during civil war? Data from the sixty-one center-seeking wars initiated from 1945 to 2014 indicate that military victory is not a prerequisite for recognition. Instead, states generally rely on a simple test: control of the capital city. Seizing the capital does not foreshadow military victory. Civil wars often continue for many years after rebels take control and receive recognition. While geopolitical and economic motives outweigh the capital control test in a small number of important cases, combatants appear to anticipate that holding the capital will be sufficient for recognition. This expectation generates perverse incentives. In effect, the international community rewards combatants for capturing or holding, by any means necessary, an area with high concentrations of critical infrastructure and civilians. In the majority of cases where rebels contest the capital, more than half of its infrastructure is damaged or the majority of civilians are displaced (or both), likely fueling long-term state weakness

Enhancement of low-temperature thermometry by strong coupling

We consider the problem of estimating the temperature T of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low T can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures—a regime which is particularly relevant to quantum technologies